The Quantum World is not Built up from Correlations

It is known that the global state of a composite quantum system can be completely determined by specifying correlations between measurements performed on subsystems only. Despite the fact that the quantum correlations thus suffice to reconstruct the quantum state, we show, using a Bell inequality argument, that they cannot be regarded as objective local properties of the composite system in question. It is well known since the work of Bell, that one cannot have locally preexistent values for all physical quantities, whether they are deterministic or stochastic. The Bell inequality argument we present here shows this is also impossible for correlations among subsystems of an individual isolated composite system. Neither of them can be used to build up a world consisting of some local realistic structure. As a corrolary to the result we argue that entanglement cannot be considered ontologically robust. The Bell inequality argument has an important advantage over others because it does not need perfect correlations but only statistical correlations. It can therefore easily be tested in currently feasible experiments using four particle entanglement.     

What Is “System”: The Information-Theoretic Arguments

The problem of “what is ‘system’?” is in the very foundations of modern quantum mechanics. Here, we point out the interest in this topic in the information-theoretic context. E.g., we point out the possibility to manipulate a pair of mutually non-interacting, non-entangled systems to employ entanglement of the newly defined “(sub)systems” consisting the one and the same composite system. Given the different divisions of a composite system into “subsystems”, the Hamiltonian of the system may generate in general non-equivalent quantum computations. Redefinition of “subsystems” of a composite system may be regarded as a method for avoiding decoherence in the quantum hardware. In principle, all the notions refer to a composite system as simple as the hydrogen atom.     

The Spectra of Quantum States and the Kronecker Coefficients of the Symmetric Group

Determining the relationship between composite systems and their subsystems is a fundamental problem in quantum physics. In this paper we consider the spectra of a bipartite quantum state and its two marginal states. To each spectrum we can associate a representation of the symmetric group defined by a Young diagram whose normalised row lengths approximate the spectrum. We show that, for allowed spectra, the representation of the composite system is contained in the tensor product of the representations of the two subsystems. This gives a new physical meaning to representations of the symmetric group. It also introduces a new way of using the machinery of group theory in quantum informational problems, which we illustrate by two simple examples.     

Partial Traces in Decoherence and in Interpretation: What Do Reduced States Refer to?

The interpretation of the concept of reduced state is a subtle issue that has relevant consequences when the task is the interpretation of quantum mechanics itself. The aim of this paper is to argue that reduced states are not the quantum states of subsystems in the same sense as quantum states are states of the whole composite system. After clearly stating the problem, our argument is developed in three stages. First, we consider the phenomenon of environment-induced decoherence as an example of the case in which the subsystems interact with each other; we show that decoherence does not solve the measurement problem precisely because the reduced state of the measuring apparatus is not its quantum state. Second, the non-interacting case is illustrated in the context of no-collapse interpretations, in which we show that certain well-known experimental results cannot be accounted for due to the fact that the reduced states of the measured system and the measuring apparatus are conceived as their quantum states. Finally, we prove that reduced states are a kind of coarse-grained states, and for this reason they cancel the correlations of the subsystem with other subsystems with which it interacts or is entangled.     

Berry phase in a composite system

The Berry phase in a composite system with one driven subsystem has been studied in this Letter. We choose two coupled spin-1 / 2 systems as the composite system; one of the subsystems is driven by a time-dependent magnetic field. We show how the Berry phases depend on the coupling between the two subsystems, and the relation between the Berry phases of the composite system and those of its subsystems.     

不确定广义组合大系统的分散输出反馈鲁棒镇定及脉冲分析

考虑了一类不确定广义组合大系统,利用Lyapunov稳定性理论和矩阵范数性质研究了该类系统的分散镇定问题.给出了一种分散输出反馈鲁棒镇定控制器的设计,得到了系统可输出反馈鲁棒镇定的不确定量的范数界.同时分析了广义组合大系统及各个孤立子系统的脉冲控制问题,给出了其闭环系统无脉冲的不确定量的范数界.最后获得了广义组合大系统及各个孤立子系统的闭环系统同时渐近稳定和无脉冲的范数界. 关键词： 广义系统 鲁棒镇定 分散控制 脉冲能观     

Quantum dissonance induced by a thermal field and its dynamics in dissipative systems

In this paper, we study quantum correlation in separable systems termed quantum dissonance [K. Modi, T. Paterek, W. Son, V. Vedral, M. Williamson, Phys. Rev. Lett. 104, 080501 (2010)]. Firstly, we study the emergence of quantum dissonance between two atoms prepared in uncorrelated states and coupled to a single-mode thermal field. We show that even for situations when the thermal field cannot entangle the two atoms, it can nevertheless induce quantum dissonance between them. Then, we investigate the dynamics including the transfer in both Markovian and non-Markovian regimes of quantum dissonance due to dissipation modeled by two independent subsystems each of which consists of a leaky cavity containing a two-level atom and surrounded by a reservoir. The two subsystems possess some amount of atomic quantum dissonance at the beginning but do not interact with each other by any means later on. We show that the quantum dissonance can be transferred among the composite subsystems, but the way it evolves and is transferred may be very different compared to that of entanglement. Finally, we present an efficient method to refrain the unwanted transfer of quantum dissonance from interested systems to reservoirs.     

Classical signal model for quantum channels

Recently it was shown that the main distinguishing features of quantum mechanics (QM) can be reproduced by a model based on classical random fields, the so-called prequantum classical statistical field theory (PCSFT). This model provides a possibility to represent averages of quantum observables, including correlations of observables on subsystems of a composite system (e.g., entangled systems), as averages with respect to fluctuations of classical (Gaussian) random fields. We consider some consequences of the PCSFT for quantum information theory. They are based on our previous observation that classical Gaussian channels (important in classical signal theory) can be represented as quantum channels. Now we show that quantum channels can be represented as classical linear transforms of classical Gaussian signals.     

Measuring multipartite concurrence with a single factorizable observable

We show that, for any composite system with an arbitrary number of finite-dimensional subsystems, it is possible to directly measure the multipartite concurrence of pure states by detecting only one single factorizable observable, provided that two copies of the composite state are available. This result can be immediately put into practice in trapped-ion and entangled-photon experiments.     

Classical-driving-assisted coherence dynamics and its conservation

We investigate the quantum coherence and quantum entanglement dynamics of a classical driven single atom coupled to a single-mode cavity. It is shown that the transformation between the atomic coherence and the atom-field entanglement exists, and can be improved by adjusting the classical driving field. The joint evolution of two identical single-body systems is also studied. The results show the quantum coherence transfers among composite subsystems, and the coherence conservation of composite subsystems is obtained. Moreover, the classical driving field can be used to suppress the decay of the coherence and entanglement, owing to considering the leaky cavity. The non-Markovian dynamics of the system is also discussed finally.     

Berry Phase of Composite System Induced by Time-Dependent Interaction

The Berry phase in a composite system induced by the time-dependent interaction is discussed. We choose two coupled spin-1/2 systems as the composite system： one of the subsystems is subjected to a static magnetic field, and the coupling parameters between two spins are controllable in time. We show that the time-dependent interaction can induce the Berry phase in a similar way as that a spin-1/2 system （qubit） is driven by an effective time-dependent magnetic field. Furthermore, using two consecutive cycles with opposite directions of both the static magnetic field as well as opposite signs of the coupling parameters, a nontrivial two-qubit unitary transformation purely based on Berry phases can be constructed.     

Composite behavior and multidegeneracy in high-pressure phases of Cs and Rb

The pressure-driven phases Cs III and Rb III having large unit cells are shown to be peculiar examples of commensurate modulated composites with two monatomic subsystems of striking simplicity. The two subsystems are obverse-reverse layers, symmetry related but misfitted. Modulations are smooth and describable by a few parameters within a well-defined superspace symmetry. Ab initio density-functional theory calculations show that the composite character is reflected in their physical behavior. Cs III has a low-energy mode with phason character corresponding to the relative sliding of the neighboring misfitted layers, the energy barrier being lower than 0.01 meV/atom, which is most favorable for transforming to other configurations. These phases possess a quasidegenerate energy landscape, close to the signature of incommensurate systems and quasicrystals.     

Continuous-Variable Entanglement Transfer from Cavity Field to Two Mesoscopic Josephson Junctions

We consider a composite system of two remote mesoscopic dosephson junctions interacting locally with a two-mode non-classical cavity field and investigate entanglement transfer from a bipartite continuous-variable （CV） system to a pair of localized mesoscopic dosephson junctions. We obtain analytically the time-dependent characteristic functions in the Wigner representation for the two CV subsystems, where two cases are considered for the zero and finite temperatures. Furthermore, we analyse the influences of the temperature on the period recovery of the entanglement.     

Evolution and symmetry of multipartite entanglement

We discover a simple factorization law describing how multipartite entanglement of a composite quantum system evolves when one of the subsystems undergoes an arbitrary physical process. This multipartite entanglement decay is determined uniquely by a single factor we call the entanglement resilience factor. Since the entanglement resilience factor is a function of the quantum channel alone, we find that multipartite entanglement evolves in exactly the same way as bipartite (two qudits) entanglement. For the two qubits case, our factorization law reduces to the main result of [T. Konrad, Nature Phys. 4, 99 (2008)10.1038/nphys885]. In addition, for a permutation P, we provide an operational definition of P asymmetry of entanglement, and find the conditions when a permuted version of a state can be achieved by local means.     

On different q-systems in nonextensive thermostatistics

It is known that the nonextensive statistics was originally formulated for the systems composed of subsystems having same q. In this paper, the existence of composite system with different q subsystems is investigated by fitting the power law degree distribution of air networks with q-exponential distribution. Then a possible extension the nonextensive statistics to different q systems is provided on the basis of an entropy nonadditivity rule and an unnormalized expectation of energy.     

Pairwise correlations in a three-partite quantum system from a prequantum random field

Prequantum classical statistical field theory (PCSFT) is a model that provides the possibility to represent the averages of quantum observables (including correlations of observables on subsystems of a composite system) as averages with respect to fluctuations of classical random fields. In view of the PCSFT terminology, quantum states are classical random fields. The aim of our approach is to represent all quantum probabilistic quantities by means of classical random fields. We obtain the classical-random-field representation for pairwise correlations in three-partite quantum systems. The three-partite case (surprisingly) differs substantially from the bipartite case. As an important first step, we generalized the theory developed for pure quantum states of bipartite systems to the states given by density operators.     

Parallel decoherence in composite quantum systems

For the standard quantum Brownian motion (QBM) model, we point out the occurrence of simultaneous (parallel), mutually irreducible and autonomous decoherence processes. Besides the standard Brownian particle, we show that there is at least another system undergoing the dynamics described by the QBM model. We do this by selecting the two mutually irreducible, global structures (decompositions into subsystems) of the composite system of the QBM model. The generalization of this observation is a new, challenging task in the foundations of the decoherence theory. We do not place our findings in any interpretational context.     

An automated algorithm for stability analysis of hybrid dynamical systems

There are many hybrid dynamical systems encountered in nature and in engineering, that have a large number of subsystems and a large number of switching conditions for transitions between subsystems. Bifurcation analysis of such systems poses a problem, because the detection of periodic orbits and the computation of their Floquet multipliers become difficult in such systems. In this paper we propose an algorithm to solve this problem. It is based on the computation of the fundamental solution matrix over a complete period–where the orbit may contain transitions through a large number of subsystems. The fundamental solution matrix is composed of the exponential matrices for evolution through the subsystems (considered linear time invariant in this paper) and the saltation matrices for the transitions through switching conditions. This matrix is then used to compose a Newton-Raphson search algorithm to converge on the periodic orbit. The algorithm–which has no restriction of the complexity of the system–locates the periodic orbit (stable or unstable), and at the same time computes its Floquet multipliers. The program is written in a sufficiently general way, so that it can be applied to any hybrid dynamical system.     

Information Between Quantum Systems via POVMs

The concepts of conditional entropy and information between subsystems of a composite quantum system are generalized to include arbitrary indirect measurements (POVMs). Some properties of those quantities differ from those of their classical counterparts; certain equalities and inequalities of classical information theory may be violated. PACS: 03.67.-a.     

Dynamics of geometric phase for composite quantum system under nonlocal unitary transformation: a case study of dimer system

In this paper, we explore the dynamical properties of geometric phase for a composite quantum system under the nonlocal unitary evolution. As an illustrative example, the analytical expressions of geometric phase are derived for the dimer system. We find that geometric phase presents some interesting properties with coupling strengths (corresponding to nonlocal unitary evolution), such as dynamical oscillation behavior with time evolution, monotonicity, symmetry, etc. We show that the geometric phase and entanglement have the same period for some conditions. Moreover, we discuss geometric phase of the whole system and its subsystems. Our investigations show that geometric phase can reflect some inherent properties of the system: it signals a transition from self-trapping to delocalization.